Revisiting Earth's radial seismic structure using a Bayesian neural network approach

Abstract

The gross features of seismic observations can be explained by relatively simple spherically symmetric (1-D) models of wave velocities, density and attenuation, which describe the Earth's average(radial) structure. 1-D earth models are often used as a reference for studies on Earth's thermo-chemical structure and dynamics, earthquake location determination and 3-D seismic tomographic models. Therefore, the quality of the latter is intrinsically linked to the robustness of the former. But what is the quality of such 1-D models? Seismic inverse problems are notoriously non-unique; different earth models can explain the data equally well, but may lead to incompatible interpretations of the nature of the Earth's interior and dynamics. Ideally, the assessment of solution quality is an integral part of any inverse method. The main motivation for this thesis was to investigate a means to simultaneously infer Earth structure and quantify the uncertainties in our estimates. A common (Bayesian) approach is to directly sample the posterior model probability density, as is done in Markov Chain Monte Carlo (MCMC) methods via a (guided) random walk. Here, I solve such seismological inference problems using pattern recognition and machine learning techniques. The method developed here, using articial neural networks, is exible and enables me to address specific hypotheses on Earth's structure in a robust, quantitative manner. Using normal mode splitting function coefficients and body wave travel times, I obtain complete statistical descriptions of features of radial Earth structure, in terms of elastic and anelastic structure, anisotropy and depths of major discontinuities. In general, I conclude that a lot can still be learned on 1-D Earth structure from seismic data; ideally, we do so prior to tackling the 3-D tomographic problem. An analysis of the information content suggests that the free oscillations constrain most parameters better than the body wave data. Spheroidal and toroidal mode data constrain the depth extent of the density excess in the lowermost mantle. Furthermore, I show, for the first time, that the average lower mantle is anisotropic below 1900 km depth, challenging the consensus that this part of the mantle is isotropic. It is possible to explain these seismic observations with currently available mineral physics data for lower mantle minerals. Therefore, seismic anisotropy, such as observed here, can provide constraints on mantle flow and deformation mechanisms. However, meaningful geodynamic interpretations require a full 3-D analysis to be made. Finally, I illustrate one pragmatic approach to data dimensionality reduction using autoencoder networks, as a first step towards non-linear seismic waveform inversion using encoded seismograms. The machine learning method adopted in this thesis is a pragmatic approach to solving non-linear Bayesian inverse problems. Their exibility and interpolation capabilities, in combination with the quantitative Bayesian framework, make neural networks well-suited for data sensitivity analysis and testing hypotheses on Earth structure. Rather than a replacement for Monte Carlo methods, I suggest that in the future they are used as a complementary tool, providing an initial assessment of data sensitivity and a lower bound on the information on model parameters that is contained in the data.